A Category-theoretical Meta-analysis of Definitions of Disentanglement

Yivan Zhang, Masashi Sugiyama
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:41596-41612, 2023.

Abstract

Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more theoretical research is needed to fully understand the defining properties of disentanglement and how different definitions relate to each other. This paper presents a meta-analysis of existing definitions of disentanglement, using category theory as a unifying and rigorous framework. We propose that the concepts of the cartesian and monoidal products should serve as the core of disentanglement. With these core concepts, we show the similarities and crucial differences in dealing with (i) functions, (ii) equivariant maps, (iii) relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our understanding of disentanglement and its various formulations and can help researchers navigate different definitions and choose the most appropriate one for their specific context.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-zhang23ak, title = {A Category-theoretical Meta-analysis of Definitions of Disentanglement}, author = {Zhang, Yivan and Sugiyama, Masashi}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {41596--41612}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/zhang23ak/zhang23ak.pdf}, url = {https://proceedings.mlr.press/v202/zhang23ak.html}, abstract = {Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more theoretical research is needed to fully understand the defining properties of disentanglement and how different definitions relate to each other. This paper presents a meta-analysis of existing definitions of disentanglement, using category theory as a unifying and rigorous framework. We propose that the concepts of the cartesian and monoidal products should serve as the core of disentanglement. With these core concepts, we show the similarities and crucial differences in dealing with (i) functions, (ii) equivariant maps, (iii) relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our understanding of disentanglement and its various formulations and can help researchers navigate different definitions and choose the most appropriate one for their specific context.} }
Endnote
%0 Conference Paper %T A Category-theoretical Meta-analysis of Definitions of Disentanglement %A Yivan Zhang %A Masashi Sugiyama %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-zhang23ak %I PMLR %P 41596--41612 %U https://proceedings.mlr.press/v202/zhang23ak.html %V 202 %X Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more theoretical research is needed to fully understand the defining properties of disentanglement and how different definitions relate to each other. This paper presents a meta-analysis of existing definitions of disentanglement, using category theory as a unifying and rigorous framework. We propose that the concepts of the cartesian and monoidal products should serve as the core of disentanglement. With these core concepts, we show the similarities and crucial differences in dealing with (i) functions, (ii) equivariant maps, (iii) relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our understanding of disentanglement and its various formulations and can help researchers navigate different definitions and choose the most appropriate one for their specific context.
APA
Zhang, Y. & Sugiyama, M.. (2023). A Category-theoretical Meta-analysis of Definitions of Disentanglement. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:41596-41612 Available from https://proceedings.mlr.press/v202/zhang23ak.html.

Related Material